The team said Thursday that Cueto has a Grade 1 strain beneath his pitching shoulder. A corresponding roster move will be made Friday.
Cueto exited in the sixth inning of his start Wednesday against Cincinnati. He wound up as the winner in a 3-0 victory and improved to 2-0 this season.
The 35-year-old Cueto left after striking out Nick Castellanos. The pitcher motioned to the Giants dugout and walked to the clubhouse, accompanied by a member of the training staff.